摘要 |
A method reduces errors in two-way ranging between transceivers due to a frequency offset. A first transceiver measures a time CA1 between transmitting a request frame and receiving a reply frame, and a time CA2 between receiving a first information bit of the reply frame and receiving a last information bit of the reply frame. A second transceiver measures a time CB2 between receiving the request frame and transmitting the last information bit of the reply frame, and a time CB1 between receiving a first information bit of the request frame and a last information bit of the request frame. A correction factor <maths id="MATH-US-00001" num="00001"> <math overflow="scroll"> <mrow> <msub> <mi>alpha</mi> <mi>c</mi> </msub> <mo>=</mo> <msqrt> <mfrac> <msub> <mi>C</mi> <mrow> <mi>B</mi> <mo></mo> <mstyle> <mspace width="0.3em" height="0.3ex"/> </mstyle> <mo></mo> <mn>1</mn> </mrow> </msub> <msub> <mi>C</mi> <mrow> <mi>A</mi> <mo></mo> <mstyle> <mspace width="0.3em" height="0.3ex"/> </mstyle> <mo></mo> <mn>2</mn> </mrow> </msub> </mfrac> </msqrt> </mrow> </math> </maths> is applied according to <maths id="MATH-US-00002" num="00002"> <math overflow="scroll"> <mrow> <mrow> <msub> <mover> <mi>C</mi> <mo>^</mo> </mover> <mrow> <mi>B</mi> <mo></mo> <mstyle> <mspace width="0.3em" height="0.3ex"/> </mstyle> <mo></mo> <mn>2</mn> </mrow> </msub> <mo>=</mo> <mrow> <msub> <mi>C</mi> <mrow> <mi>B</mi> <mo></mo> <mstyle> <mspace width="0.3em" height="0.3ex"/> </mstyle> <mo></mo> <mn>2</mn> </mrow> </msub> <mo>/</mo> <msub> <mi>alpha</mi> <mi>c</mi> </msub> </mrow> </mrow> <mo>,</mo> </mrow> </math> </maths> and the one-way time is <maths id="MATH-US-00003" num="00003"> <math overflow="scroll"> <mrow> <msub> <mover> <mi>T</mi> <mo>^</mo> </mover> <mi>t</mi> </msub> <mo>=</mo> <mrow> <mfrac> <mrow> <msub> <mi>C</mi> <mrow> <mi>A</mi> <mo></mo> <mstyle> <mspace width="0.3em" height="0.3ex"/> </mstyle> <mo></mo> <mn>1</mn> </mrow> </msub> <mo>-</mo> <msub> <mover> <mi>C</mi> <mo>^</mo> </mover> <mrow> <mi>B</mi> <mo></mo> <mstyle> <mspace width="0.3em" height="0.3ex"/> </mstyle> <mo></mo> <mn>2</mn> </mrow> </msub> </mrow> <mn>2</mn> </mfrac> <mo></mo> <mrow> <msub> <mi>T</mi> <mi>i</mi> </msub> <mo>.</mo> </mrow> </mrow> </mrow> </math> </maths> where Ti is an ideal period of the clocks of the transceivers.
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